Equalizer for a receiver in a wireless communication system

ABSTRACT

Techniques for performing equalization at a receiver are described. In an aspect, equalization is performed by sub-sampling an over-sampled input signal to obtain multiple sub-sampled signals. An over-sampled channel impulse response estimate is derived and sub-sampled to obtain multiple sub-sampled channel impulse response estimates. At least one set of equalizer coefficients is derived based on at least one sub-sampled channel impulse response estimate. At least one sub-sampled signal is filtered with the at least one set of equalizer coefficients to obtain at least one output signal. One sub-sampled signal (e.g., with largest energy) may be selected and equalized based on a set of equalizer coefficients derived from an associated sub-sampled channel impulse response estimate. Alternatively, the multiple sub-sampled signals may be equalized based on multiple sets of equalizer coefficients, which may be derived separately or jointly. The equalizer coefficients may be derived in the time domain or frequency domain.

The present application claims priority to provisional U.S. ApplicationSer. No. 60/737,459, entitled “FFT Based Methods for Equalization ofWCDMA Downlink Signals,” filed Nov. 15, 2005, assigned to the assigneehereof and incorporated herein by reference.

BACKGROUND

I. Field

The present disclosure relates generally to communication, and morespecifically to techniques for receiving a signal in a wirelesscommunication system.

II. Background

Wireless communication systems are widely deployed to provide variouscommunication services such as voice, packet data, video, broadcast,messaging, and so on. These systems may be multiple-access systemscapable of supporting communication for multiple users by sharing theavailable system resources. Examples of such multiple-access systemsinclude Code Division Multiple Access (CDMA) systems, Time DivisionMultiple Access (TDMA) systems, and Frequency Division Multiple Access(FDMA) systems.

A wireless device (e.g., a cellular phone) in a CDMA system typicallyemploys a rake receiver. The rake receiver includes one or more searcherelements and multiple demodulation elements, which are commonly referredto as searchers and fingers, respectively. Due to the relatively widebandwidth of a CDMA signal, a wireless communication channel is assumedto be composed of a finite number of resolvable signal paths, ormultipaths. Each multipath is characterized by a particular complex gainand a particular time delay. The searcher(s) search for strongmultipaths in a received signal, and fingers are assigned to thestrongest multipaths found by the searcher(s). Each finger processes itsassigned multipath and provides symbol estimates for that multipath. Thesymbol estimates from all assigned fingers are then combined to obtainfinal symbol estimates. The rake receiver can provide acceptableperformance for a CDMA system operating at lowsignal-to-interference-and-noise ratios (SNRs).

The rake receiver has a number of shortcomings. First, the rake receiveris not able to effectively handle multipaths with time delays separatedby less than one chip period, which is often referred to as a “fat-path”scenario. Second, the rake receiver typically provides suboptimalperformance at high geometry, which corresponds to high SNRs. Third,complicated circuitry and control functions are normally needed tosearch the received signal to find strong multipaths, to assign fingersto newly found multipaths, and to de-assign fingers from vanishingmultipaths.

There is therefore a need in the art for a receiver that can amelioratethe shortcomings of a rake receiver.

SUMMARY

Techniques for performing equalization at a receiver (e.g., a wirelessdevice or a base station) in a wireless communication system aredescribed herein. In one aspect, equalization is performed bysub-sampling an over-sampled input signal to obtain multiple sub-sampledsignals. An over-sampled channel estimate (e.g., an over-sampled channelimpulse response estimate) may be derived and sub-sampled to obtainmultiple sub-sampled channel estimates. For example, the input signaland the channel estimate may be over-sampled at multiple times chiprate, and the sub-sampled signals and the sub-sampled channel estimatesmay be at chip rate and may correspond to different sampling timeinstants. At least one set of equalizer coefficients is derived based onat least one sub-sampled channel estimate. At least one sub-sampledsignal is then filtered with the at least one set of equalizercoefficients to obtain at least one output signal. In one embodiment,one sub-sampled signal (e.g., with the largest energy) is selected forequalization and is filtered with a set of equalizer coefficientsderived based on an associated sub-sampled channel estimate. In otherembodiments, the multiple sub-sampled signals are equalized based onmultiple sets of equalizer coefficients, which may be derived separatelyor jointly based on the multiple sub-sampled channel estimates.

In another aspect, equalization is performed on an over-sampled inputsignal based on equalizer coefficients derived in the frequency domain.A channel impulse response estimate is derived and transformed to obtaina channel frequency response estimate. Time-domain covariance values forinput samples may be determined and transformed to obtainfrequency-domain covariance values. Frequency-domain equalizercoefficients are derived based on the channel frequency responseestimate and the frequency-domain covariance values. Thefrequency-domain equalizer coefficients are transformed to obtaintime-domain equalizer coefficients, which are used to filter the inputsamples.

Various aspects and embodiments of the invention are described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and nature of the present invention will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings in which like reference charactersidentify correspondingly throughout.

FIG. 1 shows a transmission in a wireless communication system.

FIG. 2 shows a block diagram of a base station and a wireless device.

FIG. 3 shows a block diagram of a CDMA modulator at the base station.

FIG. 4 shows a block diagram of an equalizer at the wireless device.

FIGS. 5A and 5B show a sub-sampler and sub-sampling, respectively.

FIG. 6 shows a computation unit for selective equalization.

FIG. 7 shows a process for performing selective equalization.

FIGS. 8A and 8B show computation units for separate equalization withequal and weighted combining, respectively.

FIG. 9 shows a process for performing separate equalization withcombining.

FIG. 10 shows a computation unit for joint equalization.

FIG. 11 shows a process for performing joint equalization.

FIG. 12 shows a process for performing equalization with sub-sampling.

FIG. 13 shows a process for performing equalization with coefficientsderived in the frequency domain

FIG. 14 shows a base station with multiple transmit antennas.

FIG. 15 shows a wireless device with multiple receive antennas.

FIG. 16 shows a base station using space-time transmit diversity (STTD).

DETAILED DESCRIPTION

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

FIG. 1 shows an exemplary transmission in a wireless communicationsystem. For simplicity, FIG. 1 shows only one base station 110 and onewireless device 120. A base station is generally a fixed station thatcommunicates with the wireless devices and may also be called a Node B,an access point, or some other terminology. A wireless device may befixed or mobile and may also be called a user equipment (UE), a mobilestation, a user terminal, a subscriber unit, or some other terminology.A wireless device may be a cellular phone, a personal digital assistant(PDA), a wireless modem card, or some other device or apparatus.

Base station 110 transmits a radio frequency (RF) signal to wirelessdevice 120. This RF signal may reach wireless device 120 via one or moresignal paths, which may include a direct path and/or reflected paths.The reflected paths are created by reflections of radio waves due toobstructions (e.g., buildings, trees, vehicles, and other structures) inthe wireless environment. Wireless device 120 may receive multipleinstances or copies of the transmitted RF signal. Each received signalinstance is obtained via a different signal path and has a particularcomplex gain and a particular time delay determined by that signal path.The received RF signal at wireless device 120 is a superposition of allreceived signal instances at the wireless device. Wireless device 120may also receive interfering transmissions from other transmittingstations. The interfering transmissions are shown by dashed lines inFIG. 1.

The equalization techniques described herein may be used for variouscommunication systems such as CDMA, TDMA, FDMA, orthogonal frequencydivision multiple access (OFDMA), and single-carrier FDMA (SC-FDMA)systems. A CDMA system may implement one or more radio accesstechnologies (RATs) such as cdma2000, Wideband-CDMA (W-CDMA), and so on.cdma2000 covers IS-2000, IS-856, and IS-95 standards. A TDMA system mayimplement a RAT such as Global System for Mobile Communications (GSM).These various RATs and standards are known in the art. W-CDMA and GSMare described in documents from a consortium named “3rd GenerationPartnership Project” (3GPP). cdma2000 is described in documents from aconsortium named “3rd Generation Partnership Project 2”(3GPP2). 3GPP and3GPP2 documents are publicly available. An OFDMA system transmitsmodulation symbols in the frequency domain on orthogonal frequencysubcarriers using OFDM. An SC-FDMA system transmits modulation symbolsin the time domain on orthogonal frequency subcarriers.

The equalization techniques described herein may also be used for awireless device as well as a base station. For clarity, these techniquesare described below for a wireless device in a CDMA system, which may bea W-CDMA system or a cdma2000 system. Certain portions of thedescription are for a W-CDMA system.

FIG. 2 shows a block diagram of base station 110 and wireless device120. At base station 110, a transmit (TX) data processor 210 receivestraffic data for the wireless devices being served, processes (e.g.,encodes, interleaves, and symbol maps) the traffic data to generate datasymbols, and provides the data symbols to a CDMA modulator 220. As usedherein, a data symbol is a modulation symbol for data, a pilot symbol isa modulation symbol for pilot, a modulation symbol is a complex valuefor a point in a signal constellation (e.g., for M-PSK, M-QAM, and soon), a symbol, is generally a complex value, and pilot is data that isknown a priori by both the base station and the wireless device. CDMAmodulator 220 processes the data symbols and pilot symbols as describedbelow and provides output chips to a transmitter (TMTR) 230. Transmitter230 processes (e.g., converts to analog, amplifies, filters, andfrequency upconverts) the output chips and generates an RF signal, whichis transmitted from an antenna 232.

At wireless device 120, an antenna 252 receives the transmitted RFsignal via direct and/or reflected paths and provides a received RFsignal to a receiver (RCVR) 254. Receiver 254 processes (e.g., filters,amplifies, frequency downconverts, and digitizes) the received RF signalto obtain received samples. Receiver 254 may also perform pre-processingon the received samples and provides input samples to an equalizer 260.The pre-processing may include, e.g., automatic gain control (AGC),frequency correction, digital filtering, sample rate conversion, and soon. Equalizer 260 performs equalization on the input samples asdescribed below and provides output samples. A CDMA demodulator (Demod)270 processes the output samples in a manner complementary to theprocessing by CDMA modulator 220 and provides symbol estimates, whichare estimates of the data symbols sent by base station 110 to wirelessdevice 120. A receive (RX) data processor 280 processes (e.g., symboldemaps, deinterleaves, and decodes) the symbol estimates and providesdecoded data. In general, the processing by CDMA demodulator 270 and RXdata processor 280 is complementary to the processing by CDMA modulator220 and TX data processor 210, respectively, at base station 110.

Controllers/processors 240 and 290 direct operation of variousprocessing units at base station 110 and wireless device 120,respectively. Memories 242 and 292 store data and program codes for basestation 110 and wireless device 120, respectively.

For CDMA, multiple orthogonal channels may be obtained with differentorthogonal codes. For example, multiple orthogonal physical channels areobtained with different orthogonal variable spreading factor (OVSF)codes in W-CDMA, and multiple orthogonal traffic channels are obtainedwith different Walsh codes in cdma2000. The orthogonal channels may beused to send different types of data (e.g., traffic data, control data,broadcast data, pilot, and so on) and/or traffic data for differentwireless devices.

FIG. 3 shows a block diagram of CDMA modulator 220 at base station 110.For clarity, the following description is for W-CDMA. CDMA modulator 220includes a physical channel processor 310 for each physical channel usedfor traffic data and a pilot channel processor 320 for pilot. Withinprocessor 310 for physical channel i used for wireless device 120, aspreader 312 spreads data symbols with an OVSF code o_(i)(n) forphysical channel i and provides data chips. Spreader 312 repeats eachdata symbol multiple times to generate N replicated symbols, where N isthe length of OVSF code o_(i)(n). Spreader 312 then multiplies the Nreplicated symbols with the N chips of OVSF code o_(i)(n) to generate Ndata chips for the data symbol. A scrambler 314 multiplies the datachips with a scrambling sequence s_(p)(n) for base station 110. Amultiplier 316 scales the output of scrambler 314 and provides outputchips x(n) for physical channel i.

Within pilot channel processor 320, a spreader 322 spreads pilot symbolswith an OVSF code o_(p)(n) for pilot, which is a sequence of all zeros,and provides pilot chips. A scrambler 324 multiplies the pilot chipswith the scrambling sequence s_(p)(n). A multiplier 326 scales theoutput of scrambler 324 and provides output chips p(n) for the pilotchannel. A summer 330 sums the output chips for all physical channelsand provides output chips z(n) for base station 110. The chip rate is3.84 mega-chips/second (Mcps) for W-CDMA and is 1.2288 Mcps forcdma2000.

At wireless device 120, the time-domain input samples from receiver 254may be expressed as:

$\begin{matrix}\begin{matrix}{{y(n)} = {{{h(n)} \otimes {x(n)}} + {w(n)}}} \\{{= {{\sum\limits_{i = {- \infty}}^{\infty}{{h(i)} \cdot {x\left( {n - i} \right)}}} + {w(n)}}},}\end{matrix} & {{Eq}\mspace{20mu}(1)}\end{matrix}$where x(n) is the signal component of interest for wireless device 120,

-   -   h(n) is an impulse response of the wireless channel between base        station 110 and wireless device 120,    -   w(n) is the total noise and interference observed by the desired        signal x(n),    -   y(n) is the input samples at wireless device 120, and    -   {circle around (x)} denotes a convolution.        In equation (1), w(n) includes signal components for the other        physical channels from base station 110, noise from various        sources, and interference from other transmitting stations. For        simplicity, w(n) is assumed to be additive white Gaussian noise        (AWGN) with zero mean and a variance of σ².

Equation (1) may be expressed in the frequency domain as follows:Y(ω)=H(ω)·X(ω)+W(ω),  Eq (2)where Y(ω), H(ω), X(ω) and W(ω) are frequency-domain representations ofy(n), h(n), x(n) and w(n), respectively. A frequency-domainrepresentation may be obtained by taking a discrete Fourier transform(DFT) or a fast Fourier transform (FFT) of a time-domain representation.A time-domain representation may be obtained by taking an inversediscrete Fourier transform (IDFT) or an inverse fast Fourier transform(IFFT) of a frequency-domain representation. For simplicity, the desiredsignal X(ω) is assumed to be white with unit power. The whitenessassumption is reasonable because of the scrambling with thepseudo-random scrambling sequence s_(p)(n) at base station 110.

An estimate of the desired signal X(ω) may be obtained based on a linearminimum mean square error (LMMSE) technique, as follows:

$\begin{matrix}\begin{matrix}{{\hat{X}(\omega)} = {\frac{H^{*}(\omega)}{{{H(\omega)}}^{2} + \sigma^{2}} \cdot {Y(\omega)}}} \\{{= {{C(\omega)} \cdot {.{Y(\omega)}}}},}\end{matrix} & {{Eq}\mspace{20mu}(3)}\end{matrix}$where C(ω) is an LMMSE filter response, {circumflex over (X)}(ω) is anestimate of X(ω), and “*” denotes a complex conjugate. As shown inequation (3), when σ²≈0 for high geometry, the LMMSE filter responsebecomes C(ω)≈1/H(ω), and the LMMSE filter inverts the channel. Thisresults in elimination of multipaths. When σ² is large for low geometry,the LMMSE filter response becomes C(ω)=H*(ω)/σ², and the LMMSE filterperforms matched filtering and is equivalent to a rake receiver.

The LMMSE filtering in (3) may also be performed in the time domain byconvolving the input samples with a finite impulse response (FIR) filterhaving a frequency response of C(ω), as follows:

$\begin{matrix}\begin{matrix}{{\hat{x}(n)} = {{c(n)} \otimes {y(n)}}} \\{{= {\sum\limits_{i = 1}^{2L}{{c(i)} \cdot {y\left( {n - i} \right)}}}},}\end{matrix} & {{Eq}\mspace{20mu}(4)}\end{matrix}$where c(n) and {circumflex over (x)}(n) are time-domain representationsof C(ω) and {circumflex over (X)}(ω), respectively, and 2 L is thelength of the FIR filter.

The received signal may be sampled at multiple (M) times the chip rateto obtain an over-sampled signal with M input samples for M samplingtime instants in each chip period, where in general M>1. The M samplingtime instants may be evenly spaced apart across a chip period andseparated by T_(c)/M, where T_(c) is one chip period. The over-sampledsignal may be demultiplexed or sub-sampled to obtain M sub-sampledsignals. Each sub-sampled signal contains input samples for one samplingtime instant. The input samples for each sub-sampled signal areseparated by one chip period. The quality of the sampled data isaffected by the sampling time instant. Hence, the M sub-sampled signalsmay have different qualities and may be processed as described below toobtain an improved estimate of the transmitted signal.

The over-sampled signal is not stationary, but the M sub-sampled signalsare stationary, which means that the statistics of the sub-sampledsignals do not change if the origin or start of these signals isshifted. This stationary property of the sub-sampled signals may beexploited to derive equalizer coefficients that can provide a goodestimate of the transmitted signal. The M sub-sampled signals may beviewed as M diversity branches, or simply, branches. Each branchcorresponds to a different sampling time instant. The equalizationtechniques described herein may be used with any amount of oversampling.For clarity, the equalization techniques are specifically describedbelow for the case in which the received signal is over-sampled at twicethe chip rate (or Chip×2) to obtain input samples at Chip×2.Equalization may be performed on the Chip×2 input samples as describedbelow.

FIG. 4 shows a block diagram of an embodiment of equalizer 260 in FIG.2. For this embodiment, the Chip×2 input samples y(n) are provided to achannel estimator 410 and a sub-sampler 414. Channel estimator 410derives a channel impulse response estimate h(n) for the wirelesschannel between base station 110 and wireless device 120. The channelimpulse response estimate h(n) is over-sampled and contains 2 L channeltaps that are separated by half chip period. A sub-sampler 412demultiplexes the over-sampled channel taps h(n) into on-time channeltaps h₁(n) and late channel taps h₂(n) for two sampling time instants.Similarly, sub-sampler 414 demultiplexes the Chip×2 input samples y(n)into on-time samples y₁(n) and late samples y₂(n) for the two samplingtime instants. A covariance estimator 416 determines the covariance ofthe on-time and late samples as described below and provides covariancevalues.

A computation unit 420 receives the on-time and late channel taps fromsub-sampler 412 and the covariance values from estimator 416.Computation unit 420 derives equalizer coefficients c₁(n) and c₂(n) forthe two sampling time instants based on the channel taps and thecovariance values, as described below. A FIR filter 430 filters theon-time and late samples y₁(n) and y₂(n) with the equalizer coefficientsc₁(n) and c₂(n) and provides output samples {circumflex over (x)}(n) atchip rate (or Chip×1).

FIG. 5A shows a block diagram of an embodiment of sub-sampler 414 inFIG. 4. Within sub-sampler 414, the Chip×2 input samples y(n) areprovided to a delay unit 510 and a down-sampler 514. Delay unit 510provides a delay of half chip period. A down-sampler 512 provides everyother sample from delay unit 510 as the on-time samples y₁(n).Down-sampler 514 provides every other input samples as the late samplesy₂(n). The on-time samples y₁(n) and the late samples y₂(n) are for twosampling time instants or branches and comprise all of the Chip×2 inputsamples y(n).

FIG. 5B shows the on-time samples y₁(n) and late samples y₂(n) fromsub-sampler 414. The on-time samples y₁(n) are offset by half chipperiod from the late samples y₂(n).

Referring back to FIG. 4, channel estimator 410 may derive a channelimpulse response estimate based on the pilot transmitted by base station110. In an embodiment, the channel impulse response estimate ĥ(n) may bederived as follows:

$\begin{matrix}{{{{\hat{h}(n)} = {\sum\limits_{i = 0}^{K - 1}{{y\left( {n + {2i}} \right)} \cdot {o_{p}(i)} \cdot {s_{p}^{*}(i)}}}},{for}}{{n = 1},\ldots\mspace{11mu},{2L},}} & {{Eq}\mspace{20mu}(5)}\end{matrix}$where K is an accumulation length, which is an integer multiple of thelength of the orthogonal code used for the pilot. The OVSF code for thepilot in W-CDMA has a length of 256 chips, and the Walsh code for thepilot in cdma2000 has a length of 128 chips. For equation (5), thechannel tap at index n is obtained by descrambling the input sampleswith the scrambling sequence s_(p)(n), despreading the descrambledsamples with the pilot OVSF code o_(p)(n), and accumulating over K chipperiods. The channel impulse response estimate may also be derived inother manners known in the art. For simplicity, the followingdescription assumes no channel estimation error, so that ĥ(n)=h(n).

Sub-sampler 412 demultiplexes the 2 L channel taps of the channelimpulse response estimate h(n) into L on-time channel taps h₁(n) and Llate channel taps h₂(n). Sub-sampler 412 may be implemented in the samemanner as sub-sampler 414 in FIG. 5A. The on-time channel taps h₁(n)represent the channel impulse response estimate for the on-time samplesy₁(n). The late channel taps h₂(n) represent the channel impulseresponse estimate for the late samples y₂(n).

A Chip×2 system may be considered as having a single-inputmultiple-output (SIMO) channel. The on-time and late samples may then beexpressed as:y ₁(n)=h ₁(n){circle around (x)}x ₁(n)+w ₁(n), andy ₂(n)=h ₂(n){circle around (x)}x ₂(n)+w ₂(n),  Eq (6)where w₁(n) and w₂(n) are the total noise and interference for theon-time and late samples, respectively. In general, y₁(n) and y₂(n) arejointly wide-sense stationary, which means that (1) the statistics ofeach sub-sampled signal is independent of any shift in time and (2) thejoint statistics of y₁(n) and y₂(n) are also independent of time.Equation set (6) may be expressed in the frequency domain as follows:Y ₁(ω)=H ₁(ω)·X ₁(ω)+W ₁(ω), andY ₂(ω)=H ₂(ω)·X ₂(ω)+W ₂(ω).  Eq (7)

Various equalization schemes may be used for the on-time and latesamples shown in equation sets (6) and (7). Table 1 lists someequalization schemes and a short description for each scheme. Eachequalization scheme is described in detail below.

TABLE 1 Equalization Scheme Description Selective Perform equalizationon the best branch and equalization ignore the other branch. SeparatePerform equalization on each branch separately equalization and andcombine the results for both branches. combining Joint equalizationPerform equalization on both branches jointly.

For the first two equalization schemes in Table 1, equalization may beperformed for a given branch based on an LMMSE filter derived for thatbranch. The LMMSE filter for each branch m may be expressed as:

$\begin{matrix}\begin{matrix}{{C_{m}(\omega)} = \frac{H_{m}^{*}(\omega)}{{{H_{m}(\omega)}}^{2} + \sigma^{2}}} \\{{= \frac{H_{m}^{*}(\omega)}{R_{mm}(\omega)}},} \\{{{{for}\mspace{14mu} m} = 1},2,}\end{matrix} & {{Eq}\mspace{20mu}(8)}\end{matrix}$where H_(m)(ω)) is a DFT/FFT of h_(m)(n), and

-   -   R_(mm)(ω) is a DFT/FFT of        _(mm)(τ), which is an auto-correlation of y_(m)(n).

Covariance estimator 416 in FIG. 4 may estimate the covariance of y₁(n)and y₂(n), as follows:

$\begin{matrix}{{{{\mathcal{R}_{ij}(\tau)} = {\sum\limits_{n = 1}^{K}{{y_{i}(n)} \cdot {y_{j}^{*}\left( {n - \tau} \right)}}}},{for}}{i,{j \in \left\{ {1,2} \right\}},}} & {\text{Eq}\mspace{20mu}(9)}\end{matrix}$where

_(ij)(τ) denotes the covariance between y_(i)(n) and y_(j)(n−τ), whichis a time-shifted version of y_(j)(n). As used herein, “covariance”covers both auto-correlation of a given sub-sampled signal y_(m)(n) andcross-correlation between two sub-sampled signals y₁(n) and y₂(n).

_(ij)(τ) may be derived for pertinent values of i and j and may also bederived for a range of time offsets, e.g., τ=−L/2 +1, . . . , L/2−1. Forauto-correlation,

_(mm)(τ) is symmetric so that

_(mm)(−τ)=

_(mm)* (−τ). Hence,

_(mm)(τ) may be derived for τ=0, . . . , L/2−1. The covariance may alsobe estimated in other manners known in the art.

FIG. 6 shows a block diagram of an equalizer coefficient computationunit 420 a for the selective equalization scheme. Computation unit 420 ais an embodiment of computation unit 420 in FIG. 4.

Within unit 420 a, an energy computation unit 610 receives the on-timeand late channel taps h₁(n) and h₂(n) and computes the energy E_(m) ofthe channel taps for each branch m, as follows:

$\begin{matrix}\begin{matrix}{E_{m} = {{h_{m}(n)}}^{2}} \\{{= {\sum\limits_{n = 1}^{L}{{h_{m}(n)}}^{2}}},} \\{{{{for}\mspace{14mu} m} = 1},2.}\end{matrix} & {{Eq}\mspace{20mu}(10)}\end{matrix}$

Unit 610 determines the best branch r as the branch with the largestenergy, as follows:

$\begin{matrix}{{r = {\arg\left( {\max\limits_{m}\left\{ E_{m} \right\}} \right)}},} & {{Eq}\mspace{14mu}(11)}\end{matrix}$where rε{1, 2}.

A selector 612 receives the on-time channel taps h₁(n) and the latechannel taps h₂(n) and provides the channel taps h_(r)(n) for the bestbranch r. An FFT unit 614 transforms the L channel taps h_(r)(n) to thefrequency domain with an L-point FFT and provides L channel gainsH_(r)(ω), for ω=1, . . . , L, for the best branch r. Similarly, aselector 616 receives the covariance values

₁₁(τ) for the on-time samples and the covariance values

₂₂(τ) for the late samples and provides the covariance values

_(rr)(τ) for the best branch r. An FFT unit 618 performs an L-point FFTon the covariance values, which may be arranged as {

₁₁(0), . . . ,

_(rr)(L/2−1), 0,

_(rr)* (L/2−1), . . . ,

_(rr)* (1) }, where a zero is inserted to obtain L values for the FFT.FFT unit 618 provides L frequency-domain covariance values R_(rr)(ω),for ω=1, . . . , L.

A computation unit 620 then computes frequency-domain equalizercoefficients C_(r)(ω)) for the best branch r, as follows:

$\begin{matrix}{{{{C_{r}(\omega)} = \frac{H_{r}^{*}(\omega)}{R_{rr}(\omega)}},{for}}{{\omega = 1},\ldots\mspace{11mu},{L.}}} & {{Eq}\mspace{20mu}(12)}\end{matrix}$Since R_(rr)(ω) is in the denominator, a small value for R_(rr)(ω)results in a large value for C_(r)(ω). Unit 620 may condition R_(rr)(ω)prior to computing for C_(r)(ω). For example, unit 620 may determine thelargest value of R_(rr)(ω) as

$\begin{matrix}\begin{matrix}{{{C_{r}(\omega)} = \frac{H_{r}^{*}(\omega)}{R_{rr}(\omega)}},} & {{{{for}\mspace{14mu}\omega} = 1},\ldots\mspace{11mu},{L.}}\end{matrix} & {{Eq}\mspace{14mu}(12)}\end{matrix}$identify all frequency bins ω having small values of R_(rr)(ω), e.g.,R_(rr)(ω)≦0.01×M, and set C_(r)(ω)=0 for all identified frequency bins.Alternatively, unit 620 may constrain R_(rr)(ω) to be greater than orequal to a predetermined value, e.g., R_(rr)(ω)≧0.01×M.

An IFFT unit 622 performs an L-point IFFT on the L frequency-domainequalizer coefficients C_(r)(ω) and provides L time-domain equalizercoefficients c_(r)(n) for the best branch r. A mapper 624 maps theequalizer coefficients c_(r)(n) for the best branch r to either branch 1or 2 and provides zeroed-out equalizer coefficients for the otherbranch, as follows:c ₁(n)=c _(r)(n) and c ₂(n)=0 if r=1, andc ₁(n)=0 and c ₂(n)=c _(r)(n) if r=2  Eq (13)

Referring back to FIG. 4, FIR filter 430 may filter the on-time and latesamples based on the equalizer coefficients, as follows:

$\begin{matrix}\begin{matrix}{{{\hat{x}(n)} = {{{c_{1}(n)} \otimes {y_{1}(n)}} + {{c_{2}(n)} \otimes {y_{2}(n)}}}},} \\{= {{\sum\limits_{i = 1}^{L}{{c_{1}(i)} \cdot {y_{1}\left( {n - i} \right)}}} + {\sum\limits_{i = 1}^{L}{{c_{2}(i)} \cdot {{y_{2}\left( {n - i} \right)}.}}}}}\end{matrix} & {{Eq}\mspace{20mu}(14)}\end{matrix}$All of the quantities in equation (14) are at the chip rate. For theselective equalization scheme, only equalizer coefficients c₁(n) orc₂(n) are non-zero, and only the on-time or late samples are filtered togenerate the output samples {circumflex over (x)}(n).

FIG. 7 shows a process 700 for performing equalization selectively forthe best branch. A channel impulse response estimate h(n) for a wirelesschannel is derived, e.g., based on a received pilot (block 712).Multiple (M) channel impulse response estimates h₁(n) through h_(M)(n)for M sampling time instants are derived based on (e.g., bysub-sampling) the channel impulse response estimate h(n) (block 714). Mmay be equal to two, as described above, or may be greater than two. TheM sampling time instants correspond to M different branches. Onesampling time instant is selected from among the M sampling timeinstants and denoted as sampling time instant r (block 716). Theselection of the best sampling time instant may be achieved by computingthe energy of the channel taps for each sampling time instant andcomparing the energies for the M sampling time instants to determine thesampling time instant with the largest energy.

A channel frequency response estimate H_(r)(ω) for the selected samplingtime instant is derived based on (e.g., by performing an FFT on) thechannel impulse response estimate h_(r)(n) for the selected samplingtime instant (block 718). Time-domain covariance values

_(rr)(τ) for input samples y_(r)(n) for the selected sampling timeinstant are determined, e.g., as shown in equation (9) (block 720).Frequency-domain covariance values R_(rr)(ω) are determined based on(e.g., by performing an FFT on) the time-domain covariance values

_(rr)(τ) (block 722). Frequency-domain equalizer coefficients C_(r)(ω)for the selected sampling time instant are then derived based on thechannel frequency response estimate H_(r)(ω) and the frequency-domaincovariance values R_(rr)(ω) (block 724). The equalizer coefficients maybe computed based on the LMMSE technique, as shown in equation (12), orbased on some other equalization technique. Time-domain equalizercoefficients c_(r)(n) for the selected sampling time instant aredetermined based on (e.g., by performing an IFFT on) thefrequency-domain equalizer coefficients C_(r)(ω) (block 726). The inputsamples y_(r)(n) for the selected sampling time instant are filteredwith the time-domain equalizer coefficients c_(r)(n) (block 728).

FIG. 8A shows a block diagram of an equalizer coefficient computationunit 420 b for the separate equalization with combining scheme.Computation unit 420 b performs equal combining of the two branches andis another embodiment of computation unit 420 in FIG. 4.

Within unit 420 b, an FFT unit 810 transforms the on-time channel tapsh₁(n) with an L-point FFT and provides L channel gains H₁(ω) for branch1. An FFT unit 812 transforms the late channel taps h₂(n) with anL-point FFT and provides L channel gains H₂(ω) for branch 2. An FFT unit814 performs an L-point FFT on time-domain covariance values

₁₁(τ) for branch 1, which may be arranged as {

₁₁(0), . . . ,

₁₁(L/2−1), 0,

₁₁* (L/2−1), . . . ,

₁₁* (1) }, and provides L frequency-domain covariance values R₁₁(ω), forω=1, . . . , L. An FFT unit 816 performs an L-point FFT on time-domaincovariance values

₂₂ (τ) for branch 2, which may be arranged as {

₂₂(0), . . . ,

₂₂(L/2−1), 0,

₂₂* (L/2−1), . . . ,

₂₂* (1) }, and provides L covariance values R₂₂(6)), for ω=1, . . . , L.

A computation unit 820 computes frequency-domain equalizer coefficientsC₁(ω) for branch 1 based on the channel gains H₁(ω) and the covariancevalues R₁₁(ω) for branch 1, e.g., as shown in equation (12). Similarly,a computation unit 822 computes frequency-domain equalizer coefficientsC₂(ω) for branch 2 based on the channel gains H₂(ω) and the covariancevalues R₂₂(ω) for branch 2. An IFFT unit 830 performs an L-point IFFT onthe L frequency-domain equalizer coefficients C₁(ω) and provides Ltime-domain equalizer coefficients c₁(n) for branch 1. An IFFT unit 832performs an L-point IFFT on the L frequency-domain equalizercoefficients C₂(ω) and provides L time-domain equalizer coefficientsc₂(n) for branch 2. The equalizer coefficients c₁(n) and c₂(n) are usedto filter the on-time samples y₁(n) and the late samples c₂(n), as shownin equation (14).

FIG. 8B shows a block diagram of an equalizer coefficient computationunit 420 c for the separate equalization with combining scheme.Computation unit 420 c performs weighted combining of the two branchesand is yet another embodiment of computation unit 420 in FIG. 4.Computation unit 420 c includes FFT units 810, 812, 814 and 816,coefficient computation units 820 and 822, and IFFT units 830 and 832that operate as described above for FIG. 8A. Computation unit 420 cfurther includes weight computation units 824 and 826 and multipliers834 and 836.

Unit 824 receives the on-time channel taps h₁(n) and computes the weightfor branch 1. Unit 826 receives the late channel taps h₂(n) and computesthe weight for branch 2. The weight q_(m) for each branch m may becomputed as follows:

$\begin{matrix}\begin{matrix}{q_{m} = \sqrt{{{h_{m}(n)}}^{2}}} \\{{= \left( {\sum\limits_{n = 1}^{L}{{h_{m}(n)}}^{2}} \right)^{1/2}},} \\{{{{for}\mspace{14mu} m} = 1},2.}\end{matrix} & {{Eq}\mspace{20mu}(15)}\end{matrix}$In equation (15), the scaling by L is omitted since both branches areaffected by the same scaling.

The coefficients for each branch are scaled by the weight for thatbranch. For the embodiment shown in FIG. 8B, the scaling is performed onthe time-domain equalizer coefficients. Multiplier 834 is located afterIFFT unit 830, scales each time-domain equalizer coefficient c₁′(n) fromFFT unit 830 with the weight q₁ for branch 1, and provides L outputequalizer coefficients c₁(n) for branch 1. Similarly, multiplier 836 islocated after IFFT unit 832, scales each time-domain coefficient c₂′(n)from FFT unit 832 with the weight q₂ for branch 2, and provides L outputequalizer coefficients c₂(n) for branch 2. In another embodiment, whichis not shown in FIG. 8B, the scaling is performed on thefrequency-domain equalizer coefficients C_(m)(ω). For this embodiment,multipliers 834 and 836 would be located after computation units 820 and822, respectively.

FIG. 9 shows a process 900 for performing equalization separately foreach branch and combining the results. A channel impulse responseestimate h₁(n) for a wireless channel is derived, e.g., based on areceived pilot (block 912). A first channel impulse response estimateh₁(n) for a first sampling time instant and a second channel impulseresponse estimate h₂(n) for a second sampling time instant are derivedbased on (e.g., by sub-sampling) the channel impulse response estimateh(n) (block 914). A first channel frequency response estimate H₁(ω) forthe first sampling time instant is derived based on (e.g., by performingan FFT on) the first channel impulse response estimate h₁(n) (block916). A second channel frequency response estimate H₂(ω) for the secondsampling time instant is derived based on the second channel impulseresponse estimate h₂(n) (also block 916). Time-domain covariance values

₁₁(τ) for input samples y₁(n) for the first sampling time instant andtime-domain covariance values

₂₂(τ) for input samples y₂(n) for the second sampling time instant aredetermined (block 918). Frequency-domain covariance values R₁₁(ω) forthe first sampling time instant are determined based on (e.g., byperforming an FFT on) the time-domain covariance values

₁₁(τ) (block 920). Frequency-domain covariance values R₂₂(ω) for thesecond sampling time instant are determined based on the time-domaincovariance values

₂₂(τ) (also block 920). Frequency-domain equalizer coefficients C₁(ω)for the first sampling time instant are derived based on the channelfrequency response estimate H₁(ω) and the frequency-domain covariancevalues R₁₁(ω) (block 922). Frequency-domain equalizer coefficients C₂(ω)for the second sampling time instant are derived based on the channelfrequency response estimate H₂(ω) and the frequency-domain covariancevalues R₂₂(ω) (also block 922). The equalizer coefficients may becomputed based on the LMMSE technique, as shown in equation (12), orbased on some other equalization technique.

Time-domain equalizer coefficients c₁′(n) for the first sampling timeinstant are determined based on (e.g., by performing an IFFT on) thefrequency-domain equalizer coefficients C₁(ω) (block 924). Time-domainequalizer coefficients c₂′(n) for the second sampling time instant aredetermined based on the frequency-domain equalizer coefficients C₂(ω)(also block 924). The time-domain equalizer coefficients c₁′(n) for thefirst sampling time instant are scaled by a first weight q₁ to obtainoutput equalizer coefficient c₁(n) (block 926). The time-domainequalizer coefficients c₂′(n) for the second sampling time instant arescaled by a second weight q₂ to obtain output equalizer coefficientc₂(n) (also block 926). The first and second weights may be equal or maybe derived based on the energies of h₁(n) and h₂(n), respectively. Theinput samples are filtered with the output equalizer coefficients c₁(n)and c₂(n) (block 928).

FIG. 10 shows a block diagram of an equalizer coefficient computationunit 420 d for the joint equalization scheme. Computation unit 420 d isyet another embodiment of computation unit 420 in FIG. 4.

Within unit 420 d, an FFT unit 1010 transforms the on-time channel tapsh₁(n) and provides L channel gains H₁(ω) for branch 1. An FFT unit 1012transforms the late channel taps h₂(n) and provides L channel gainsH₂(ω) for branch 2. An FFT unit 1014 performs an L-point FFT ontime-domain covariance values R₁₁(τ), which may be arranged as {

₁₁(0), . . . ,

₁₁(L/2−1) , 0,

₁₁*(L/2−1), . . . ,

₁₁*(1) }, and provides L frequency-domain covariance values R₁₁(ω), forω=1, . . . , L. An FFT unit 1016 performs an L-point FFT on time-domaincovariance values R₂₂(τ), which may be arranged as {

₂₂ (0), . . . ,

₂₂*(L/2−1), 0,

₂₂*(L/2−1), . . . ,

*₂₂(1) }, and provides L covariance values R₂₂(ω), for ω=1, . . . , L.An FFT unit 1018 performs an L-point FFT on L time-domain covariancevalues R₁₂(τ), which may be arranged as {

₁₂(0), . . . ,

₁₂(L/2−1), 0,

₂₂(−L/2+1), . . . ,

₂₂(−1)}, and provides L covariance values R₁₂(ω), for ω=1, . . . , L.

A computation unit 1020 jointly computes the frequency-domain equalizercoefficients C₁(ω) and C₂(ω) for branches 1 and 2, as described below.An IFFT unit 1030 transforms the frequency-domain equalizer coefficientsC₁(ω) and provides time-domain equalizer coefficients c₁(n) for branch1. An IFFT unit 1032 transforms the frequency-domain equalizercoefficients C₂(ω) and provides time-domain equalizer coefficients c₂(n)for branch 2.

For the joint equalization scheme, the on-time and late samples y₁(n)and y₂(n) are equalized with two sets of equalizer coefficients c₁(n)and c₂(n) that are derived jointly such that the output samples{circumflex over (x)}(n) in equation (14) provide the best linearapproximation of x(n) in the mean square error sense. The LMMSEsolutions for the two sets of equalizer coefficients may be expressed inthe frequency domain, as follows:

$\begin{matrix}{\begin{bmatrix}{C_{1}(\omega)} \\{C_{2}(\omega)}\end{bmatrix} = {\begin{bmatrix}{R_{11}(\omega)} & {R_{12}(\omega)} \\{R_{21}(\omega)} & {R_{22}(\omega)}\end{bmatrix}^{- 1} \cdot {\begin{bmatrix}{H_{1}^{*}(\omega)} \\{H_{2}^{*}(\omega)}\end{bmatrix}.}}} & {{Eq}\mspace{20mu}(16)}\end{matrix}$Since R₂₁(ω)=R₁₂ *(ω), it is sufficient to estimate just R₁₁(τ), R₂₂(τ)and R₁₂(τ).

In equation (16), L 2×2 matrices are formed for ω=1, . . . , L. Each 2×2matrix may be inverted and used to derive the equalizer coefficientsC₁(ω) and C₂(ω) for one frequency bin ω. A given 2×2 matrix may bepoorly conditioned, e.g., close to singular because of estimationerrors. The inversion of a poorly conditioned matrix may produce a largeentry that may excessively enhance noise. Several techniques may be usedto deal with poorly conditioned matrices.

In a first embodiment, the joint processing of the two branches isperformed with “diagonal” conditioning. For this embodiment, thetime-domain covariance values for branches 1 and 2 are conditioned bysetting

₁₁(0)=β·

₁₁(0) and

₂₂(0)=β·

₂₂ (0), where β>1.0 and may be selected as, e.g., β=1.05. This scalingfor a single tap of

_(mm)(τ) introduces a small spectral component in each frequency bin ofR_(mm)(ω), which makes the frequency domain matrices “more invertible”.FFTs are then performed on the conditioned

₁₁(τ) and

₂₂(τ) .

Computation unit 1020 may then compute the frequency-domain equalizercoefficients C₁(ω) and C₂(ω) for branches 1 and 2, respectively, asfollows:

$\begin{matrix}{\begin{bmatrix}{C_{1}(\omega)} \\{C_{2}(\omega)}\end{bmatrix} = {\frac{1}{{{R_{11}(\omega)}{R_{22}(\omega)}} - {{R_{12}(\omega)}}^{2}} \cdot \begin{bmatrix}{R_{22}(\omega)} & {- {R_{12}^{*}(\omega)}} \\{- {R_{12}(\omega)}} & {R_{11}(\omega)}\end{bmatrix} \cdot {\begin{bmatrix}{H_{1}^{*}(\omega)} \\{H_{2}^{*}(\omega)}\end{bmatrix}.}}} & {{Eq}\mspace{20mu}(17)}\end{matrix}$The scaling of

₁₁(0) and

₂₂(0) by β results in a small amount of distortion that is negligible.

In a second embodiment, the joint processing of the two branches isperformed with “pseudo-inverse” conditioning. For this embodiment, theequalizer coefficients C₁(ω) and C₂(ω) for each frequency bin ω may becomputed in one of several manners depending on whether or not the 2×2matrix for that frequency bin is poorly conditioned.

For each frequency bin ω, the following condition is determined:R ₁₁(ω)R ₂₂(ω)−|R ₁₂(ω)|²≧0.05·[R ₁₁(ω)+R ₂₂(ω)]².  Eq (18)Equation (18) checks if a “condition number” of the 2×2 matrix forfrequency bin ω is below a certain value. This condition may be used todetermine whether or not the 2×2 matrix is poorly conditioned.

For each frequency bin ω in which the 2×2 matrix is not poorlyconditioned, which is indicated by the condition in equation (18)holding, the frequency-domain equalizer coefficients C₁(ω) and C₂(ω) forthat frequency bin may be computed as shown in equation (17).

For each frequency bin ω in which the 2×2 matrix is poorly conditioned,which is indicated by the condition in equation (18) not holding, thefrequency-domain equalizer coefficients C₁(ω) and C₂(ω) for thatfrequency bin may be computed as follows. The following quantities arecomputed for frequency bin ω:

$\begin{matrix}{{{\lambda_{\max}(\omega)} = {{R_{11}(\omega)} + {R_{22}(\omega)} + {0.5 \cdot \sqrt{\left\lbrack {{R_{11}(\omega)} - {R_{22}(\omega)}} \right\rbrack^{2} + {4{R_{12}(\omega)}}}}}},} & {{Eq}\mspace{20mu}(19)} \\{{{\upsilon(\omega)} = \frac{{\lambda_{\max}(\omega)} - {R_{11}(\omega)}}{R_{12}^{*}(\omega)}},} & {{Eq}\mspace{20mu}(20)}\end{matrix}$where λ_(max)(ω) is the largest eigenvalue of the 2×2 matrix forfrequency bin ω, and

-   -   ν(ω) is a component of an eigenvector [1 ν(ω)]^(T) of the 2×2        matrix.

The frequency-domain equalizer coefficients C₁(ω) and C₂(ω) forfrequency bin ω may then be computed as follows:

$\begin{matrix}{\begin{bmatrix}{C_{1}(\omega)} \\{C_{2}(\omega)}\end{bmatrix} = {\frac{1}{{\lambda_{\max}(\omega)} \cdot \left( {1 + {{\upsilon(\omega)}}^{2}} \right)} \cdot \begin{bmatrix}1 & {\upsilon(\omega)} \\{\upsilon^{*}(\omega)} & {{\upsilon(\omega)}}^{2}\end{bmatrix} \cdot {\begin{bmatrix}{H_{1}^{*}(\omega)} \\{H_{2}^{*}(\omega)}\end{bmatrix}.}}} & {{Eq}\mspace{20mu}(21)}\end{matrix}$Equation (21) essentially nulls out the smaller eigenvalue of the 2×2matrix and takes the pseudo-inverse of the resultant matrix.

Equation (21) may be approximated as follows:

$\begin{matrix}{\begin{bmatrix}{C_{1}(\omega)} \\{C_{2}(\omega)}\end{bmatrix} = {\frac{1}{\left\lbrack {{R_{11}(\omega)} + {R_{22}(\omega)}} \right\rbrack^{2}} \cdot \begin{bmatrix}{R_{11}(\omega)} & {R_{12}(\omega)} \\{R_{12}^{*}(\omega)} & {R_{22}(\omega)}\end{bmatrix} \cdot \begin{bmatrix}{H_{1}^{*}(\omega)} \\{H_{2}^{*}(\omega)}\end{bmatrix} \cdot}} & {{Eq}\mspace{20mu}(22)}\end{matrix}$

Equation (21) may also be approximated as follows:

$\begin{matrix}{{{\begin{bmatrix}{C_{1}(\omega)} \\{C_{2}(\omega)}\end{bmatrix} = {{A(\omega)} \cdot \begin{bmatrix}{{R_{12}(\omega)}}^{2} & {{R_{22}(\omega)} \cdot {R_{12}^{*}(\omega)}} \\{{R_{22}(\omega)} \cdot {R_{12}(\omega)}} & {R_{22}^{2}(\omega)}\end{bmatrix} \cdot \begin{bmatrix}{H_{1}^{*}(\omega)} \\{H_{2}^{*}(\omega)}\end{bmatrix}}},{where}}{{A(\omega)} = {\frac{1}{\left\lbrack {{R_{11}(\omega)} + {R_{22}(\omega)}} \right\rbrack \cdot \left\lbrack {{R_{22}^{2}(\omega)} + {R_{12}^{2}(\omega)}} \right\rbrack}.}}} & {{Eq}\mspace{20mu}(23)}\end{matrix}$

FIG. 11 shows a process 1100 for performing equalization jointly formultiple branches. A channel impulse response estimate h(n) for awireless channel is derived, e.g., based on a received pilot (block1112. First and second channel impulse response estimates h₁(n) andh₂(n) for first and second sampling time instants, respectively, arederived based on (e.g., by sub-sampling) the channel impulse responseestimate h(n) (block 1114). First and second channel frequency responseestimates H₁(ω) and H₂(ω) for the first and second sampling timeinstants are derived based on the first and second channel impulseresponse estimates h₁(n) and h₂(n), respectively (block 1116).Time-domain covariance values

₁₁(τ),

₂₂(τ) and

₁₂(τ) for input samples y₁(n) and y₂(n) for the first and secondsampling time instants are determined (block 1118). Frequency-domaincovariance values R₁₁(ω), R₂₂(ω) and R₁₂(ω) are determined based on thetime-domain covariance values

₁₁(τ),

₂₂(τ) and

₁₂(τ), respectively (block 1120).

Frequency-domain equalizer coefficients C₁(ω) and C₂(ω) for the firstand second sampling time instants are derived jointly based on the firstand second channel frequency response estimates H₁(ω) and H₂(ω) and thefrequency-domain covariance values R₁₁(ω), R₂₂(ω) and R₁₂(ω) (block1122). The equalizer coefficients may be computed based on the LMMSEtechnique, as shown in equations (16) through (23), or based on someother equalization technique. Time-domain equalizer coefficients c₁(n)and c₂(n) for the first and second sampling time instants are determinedbased on the frequency-domain equalizer coefficients C₁(ω) and C₂(ω),respectively (block 1124). The input samples are then filtered with thetime-domain equalizer coefficients c₁(n) and c₂(n) (block 1126).

FIG. 12 shows a process 1200 for performing equalization on anover-sampled input signal with sub-sampling. The over-sampled inputsignal is sub-sampled or demultiplexed to obtain multiple sub-sampledsignals (block 1212). An over-sampled channel estimate is derived, e.g.,based on a received pilot (block 1214). The over-sampled channelestimate may be a channel impulse response estimate that is over-sampledin time, a channel frequency response estimate that is over-sampled infrequency, and so on. The over-sampled channel estimate is sub-sampledto obtain multiple sub-sampled channel estimates (block 1216).Equalization is performed on the multiple sub-sampled signals with themultiple sub-sampled channel estimates to obtain at least one outputsignal. For the equalization, at least one set of equalizer coefficientsmay be derived based on at least one sub-sampled channel estimate usingany of the equalization schemes described above (block 1218). Theequalizer coefficients may be derived in the time domain or frequencydomain. At least one sub-sampled signal is then filtered with the atleast one set of equalizer coefficients to obtain the at least oneoutput signal (block 1220).

FIG. 13 shows a process 1300 for performing equalization on anover-sampled input signal with equalizer coefficients derived in thefrequency domain. A channel impulse response estimate is derived, e.g.,based on a received pilot (block 1312). A channel frequency responseestimate is derived based on (e.g., by performing an FFT on) the channelimpulse response estimate (block 1314). For an LMMSE filter, time-domaincovariance values for the input samples may be determined (block 1316)and transformed to obtain frequency-domain covariance values (block1318). Frequency-domain equalizer coefficients are derived for multiplefrequency bins based on the channel frequency response estimate and thefrequency-domain covariance values (block 1320). Time-domain equalizercoefficients are derived based on (e.g., by performing an IFFT on) thefrequency-domain equalizer coefficients (block 1322). The input samplesare then filtered with the time-domain equalizer coefficients to obtainoutput samples (block 1324)

For clarity, the equalization techniques have been described mostly forthe case in which the input samples y(n) are at Chip×2 and there are twobranches corresponding to two sampling time instants. In general, theequalization techniques may be used for input samples that areover-sampled at multiple (M) times the chip rate, where M≧2. M branchesmay be formed for M sampling time instants. M sequences of input samplesy₁(n) through y_(M)(n) for M sampling time instants may be obtained bysub-sampling or demultiplexing the over-sampled input samples y(n). Mchannel impulse response estimates h₁(n) through h_(M)(n) for M samplingtime instants may be obtained by sub-sampling or demultiplexing anover-sampled channel impulse response estimate h(n) for the wirelesschannel. Covariance values

_(ij)(τ), for i,jε{1, . . . , M}, may be derived based on the inputsamples y(n), e.g., as shown in equation (9).

For the selective equalization scheme, the best branch may be selected,e.g., based on the energies of the channel impulse response estimatesfor the M branches. Equalizer coefficients for the best branch may bederived based on the channel impulse response estimate and thecovariance values for that branch. The input samples for the best branchare filtered with the equalizer coefficients for that branch.

For the separate equalization with combining scheme, a set of equalizercoefficients may be derived for each branch based on the channel impulseresponse estimate and the covariance values for that branch. The M setsof equalizer coefficients for the M branches may be scaled with equalweights for all M branches or different weights determined based on theenergies for the M branches. The input samples are filtered with the Msets of equalizer coefficients for the M branches.

For the joint equalization scheme, M sets of equalizer coefficients forthe M branches may be derived jointly based on the channel impulseresponse estimates and the covariance values for all M branches. Theinput samples are filtered with the M sets of equalizer coefficients forthe M branches.

The channel impulse response estimate h(n), the covariance values

_(ij)(τ), and the equalizer coefficients c_(m)(n) may be updated at asufficient rate to achieve good performance. For example, h(n),

_(ij)(τ) and c_(m)(n) may be updated whenever a new pilot symbol isreceived, whenever a predetermined number of pilot symbols is received,in each slot, in each frame, and so on. For W-CDMA, a pilot symbol issent in 256 chips, each slot spans 2560 chips or 10 pilot symbols, andeach frame includes 15 slots. For cdma2000, a pilot symbol is sent in128 chips, each slot spans 768 chips or 6 pilot symbols, and each frameincludes 16 slots.

For clarity, the equalization techniques have been described for atransmitter with a single antenna and a receiver with a single antenna.These techniques may also be used for a transmitter with multipleantennas and for a receiver with multiple antennas, as described below.

FIG. 14 shows a block diagram of a base station 112 with two transmitantennas 1432 a and 1432 b. Within base station 112, a TX data processor1410 processes traffic data and generates data symbols. A CDMA modulator1420 processes data and pilot symbols and generates output chips z¹(n)and z²(n) for transmit antennas 1432 a and 1432 b, respectively.

Within CDMA modulator 1420, a physical channel processor 1422 processesdata symbols for physical channel i and generates output chips x(n) forthis physical channel. A pilot channel processor 1424 generates outputchips p¹(n) and p²(n) for the pilot for transmit antennas 1432 a and1432 b, respectively. Processors 1422 and 1424 may be implemented withprocessors 310 and 320, respectively, in FIG. 3. A multiplier 1426 ascales the output chips x(n) with a weight v₁ for transmit antenna 1432a and generates scaled output chips x¹(n). A multiplier 1426 b scalesthe output chips x(n) with a weight v₂ for transmit antenna 1432 b andgenerates scaled output chips x²(n). A summer 1428 a sums the outputchips for all physical channels for transmit antenna 1432 a and providesoutput chips z¹(n). A summer 1428 b sums the output chips for allphysical channels for transmit antenna 1432 b and provides output chipsz²(n). A transmitter 1430 a processes the output chips z¹(n) andgenerates a first RF signal, which is transmitted from antenna 1432 a. Atransmitter 1430 b processes the output chips z²(n) and generates asecond RF signal, which is transmitted from antenna 1432 b. Acontroller/processor 1440 directs operation at base station 112. Amemory 1442 stores data and program codes for base station 112.

For closed-loop transmit diversity (CLTD), the weights v₁ and v₂ may beselected by wireless device 120 and sent back to base station 112. Theweights v₁ and v₂ may be selected to maximize the received signal atwireless device 120. In general, the weights v₁ and v₂ may be derived bythe wireless device and/or the base station in various manners.

At wireless device 120, the input samples y(n) may be expressed as:

$\begin{matrix}\begin{matrix}{{{y(n)} = {{\left\lbrack {{v_{1} \cdot {h^{1}(n)}} + {v_{2} \cdot {h^{2}(n)}}} \right\rbrack \otimes {x(n)}} + {w(n)}}},} \\{{= {{{h_{eff}(n)} \otimes {x(n)}} + {w(n)}}},}\end{matrix} & {{Eq}\mspace{20mu}(24)}\end{matrix}$where h¹(n) is an impulse response from antenna 1432 a to wirelessdevice 120,

-   -   h²(n) is an impulse response from antenna 1432 b to wireless        device 120, and    -   h_(eff)(n)=v₁·h¹(n)+v₂·h²(n) is an effective impulse response        for the wireless channel between base station 112 and wireless        device 120.

A channel impulse response estimate h¹(n) for transmit antenna 1432 amay be derived based on the pilot p¹(n) transmitted from this antenna.Similarly, a channel impulse response estimate h²(n) for transmitantenna 1432 b may be derived based on the pilot p²(n) transmitted fromthis antenna. An effective channel impulse response estimate h_(eff)(n)may then be derived based on h¹(n) and h²(n) and the known weights v₁and v₂. h_(eff)(n) may also be derived in other manners.

The equalization techniques described above may be used with theeffective channel impulse response estimate h_(eff)(n) instead of h(n).In particular, h_(eff)(n) may be sub-sampled to obtain effective channelimpulse response estimates h_(eff,1)(n) through h_(eff,M)(n) for Mbranches corresponding to M sampling time instants. Equalization may beperformed for the best branch, separately for the M branches andcombined, or jointly for all M branches, as described above.

FIG. 15 shows a block diagram of a wireless device 122 with two receiveantennas 1552 a and 1552 b. At wireless device 122, a receiver 1554 aprocesses a first received RF signal from antenna 1552 a and providesinput samples y¹(n) for this antenna. A receiver 1554 b processes asecond received RF signal from antenna 1552 b and provides input samplesy²(n) for this antenna. An equalizer 1560 performs equalization on theinput samples y¹(n) and y²(n) as described below and provides outputsamples {circumflex over (x)}(n). A CDMA demodulator 1570 processes theoutput samples and provides symbol estimates. An RX data processor 1580processes the symbol estimates and provides decoded data. Acontroller/processor 1590 directs operation at wireless device 122. Amemory 1592 stores data and program codes for wireless device 122.

At wireless device 122, the input samples y¹(n) from receiver 1554 a andthe input samples y²(n) from receiver 1554 b may be expressed as:y ¹(n)=h ¹(n){circle around (x)}x(n)+w ¹(n) , andy ²(n)=h ²(n){circle around (x)}x(n)+w ²(n),  Eq (25)where h¹(n) is an impulse response from base station 110 to antenna 1552a,

-   -   h²(n) is an impulse response from base station 110 to antenna        1552 b, and    -   w¹(n) and w²(n) are the total noise for antennas 1552 a and 1552        b, respectively.

A channel impulse response estimate h¹(n) for receive antenna 1552 a maybe derived based on the pilot received via this antenna. Similarly, achannel impulse response estimate h²(n) for receive antenna 1552 b maybe derived based on the pilot received via this antenna. The inputsamples y^(α)(n) for each receive antenna α may be sub-sampled to obtaininput samples y₁ ^(α)(n) through y_(M) ^(α)(n) for M branches for thatantenna. If M=2, then the input samples for two branches for eachreceive antenna may be expressed as:y ₁ ¹(n)=h ₁ ¹(n){circle around (x)}x(n)+w ₁ ¹(n),y ₂ ¹(n)=h ₂ ¹(n){circle around (x)}x(n)+w ₂ ¹(n),y ₁ ²(n)=h ₁ ²(n){circle around (x)}x(n)+w ₁ ²(n), andy ₂ ²(n)=h ₂ ²(n){circle around (x)}x(n)+w ₂ ²(n),  Eq (26)where y₁ ¹(n) and y₂ ¹(n) are obtained by sub-sampling y¹(n) for antenna1552 a,

-   -   y₁ ²(n) and y₂ ²(n) are obtained by sub-sampling y²(n) for        antenna 1552 b,    -   h₁ ¹(n) and h₂ ¹(n) are obtained by sub-sampling h¹(n) for        antenna 1552 a, and    -   h₁ ²(n) and h₂ ²(n) are obtained by sub-sampling h²(n) for        antenna 1552 b.

The equalization techniques described above may be applied to the inputsamples y₁ ¹(n), y₂ ¹(n), y₁ ²(n) and y₂ ²(n) for four branches formedby two sampling time instants and two receive antennas. For theselective equalization scheme, the best branch having the largest energyamong the four branches may be selected for equalization. For theseparate equalization with combining scheme, equalization may beperformed separately for four branches, for two best branches among thefour branches, for the best branch for each receive antenna, and so on.The results for all selected branches may be combined to generate theoutput samples {circumflex over (x)}(n). For the joint equalizationscheme, equalization may be performed jointly for four branches, for twobest branches among the four branches, for two best branches for the tworeceive antennas, and so on.

In an embodiment, the best branch is determined for each receiveantenna, and equalization is performed for the two best branches for thetwo receive antennas. For this embodiment, the energy of each of thefour branches may be determined, e.g., as shown in equation (10). Foreach receive antenna α, where αε{1, 2}, the branch with more energy isselected and denoted as r(α). Input samples y_(r(1)) ¹(n) and y_(r(2))²(n) and channel impulse response estimates h_(r(1)) ¹(n) and h_(r(2))²(n) may then be processed based on any of the equalization schemesdescribed above to obtain the output samples {circumflex over (x)}(n).

FIG. 16 shows a block diagram of a base station 114 using space-timetransmit diversity (STTD). Within base station 114, a TX data processor1610 processes traffic data and generates data symbols s(l). A CDMAmodulator 1620 processes data and pilot symbols and generates outputchips z¹(n) and z²(n) for two transmit antennas 1632 a and 1632 b.

Within CDMA modulator 1620, an STTD encoder 1622 performs STTD encodingon data symbols s(l) and provides STTD encoded symbols s¹(l) and s²(l)for transmit antennas 1632 a and 1632 b, respectively. If s(l)=s₁, s₂,s₃, s₄, . . . , where s_(l) is a data symbol for symbol period l, thens¹(l)=s₁, s₂, s₃, s₄, . . . , and s²(l)=−s₂*, s₁*, −s₄*, s₃*, . . . .Physical channel processors 1624 a and 1624 b process STTD encodedsymbols s¹(l) and s²(l), respectively, and provide output chips x¹(n)and x²(n), respectively. A pilot channel processor 1626 generates outputchips p¹(n) and p²(n) for the pilot for transmit antennas 1632 a and1632 b, respectively. Processors 1624 and 1626 may be implemented withprocessors 310 and 320, respectively, in FIG. 3. Summers 1628 a and 1628b sum the output chips for all physical channels for transmit antennas1632 a and 1632 b, respectively, and provide output chips z¹(n) andz²(n), respectively. Transmitters 1630 a and 1630 b process the outputchips z¹(n) and z²(n), respectively, and generate two RF signals thatare transmitted from antennas 1632 a and 1632b, respectively. Acontroller/processor 1640 directs operation at base station 114. Amemory 1642 stores data and program codes for base station 114.

At wireless device 120, the input samples y(n) may be expressed as:y(n)=h ¹(n){circle around (x)}x ¹(n)+h ²(n){circle around (x)}x²(n)+w(n),  Eq (27)where h¹(n) is an impulse response from antenna 1632 a to wirelessdevice 120, and

-   -   h²(n) is an impulse response from antenna 1632 b to wireless        device 120.

A channel impulse response estimate h¹(n) for transmit antenna 1632 amay be derived based on the pilot p¹(n) received from this antenna. Achannel impulse response estimate h²(n) for transmit antenna 1632 b maybe derived based on the pilot p²(n) received from this antenna. If M=2,then h¹(n) may be sub-sampled to obtain h₁ ¹(n) and h₂ ¹(n), h²(n) maybe sub-sampled to obtain h₁ ²(n) and h₂ ²(n), and the input samples y(n)may be sub-sampled to obtain y₁(n) and y₂(n) for two branches. Thedesired signals x¹(n) and x²(n) may be recovered in various manners.

In one embodiment, the desired signals x¹(n) and x²(n) are recovered byperforming equalization for the best sampling time instant. For thisembodiment, the energy E₁ for the first sampling time instant iscomputed as E₁=∥h₁ ¹(n)∥²+∥h₁ ²(n)∥², the energy E₂ for the secondsampling time instant is computed as E₂=∥h₂ ¹(n)∥²+∥h₂ ²(n)∥², and thesampling time instant r with the larger energy is selected. Equalizercoefficients c_(r) ¹(n) may be computed for transmit antenna 1632 a andsampling time instant r based on h_(r) ¹(n) and possibly covariancevalues. Similarly, equalizer coefficients c_(r) ²(n) may be computed fortransmit antenna 1632 b and sampling time instant r based on h_(r) ² (n)and possibly covariance values.

Input samples y_(r)(n) for sampling time instant r are then filteredwith the equalizer coefficients c_(r) ¹(n) to obtain output samples{circumflex over (x)}¹(n), which are estimates of output chips x¹(n).The input samples y_(r)(n) are also filtered with the equalizercoefficients c_(r) ²(n) to obtain output samples {circumflex over(x)}²(n), which are estimates of output chips {circumflex over (x)}²(n).CDMA demodulation may then be performed on the output samples{circumflex over (x)}¹(n) to obtain symbol estimates ŝ¹(l), which areestimates of the STTD encoded symbols s¹(l) transmitted from antenna1632 a. CDMA demodulation may also be performed on the output samples{circumflex over (x)}²(n) to obtain symbol estimates ŝ²(l), which areestimates of the STTD encoded symbols s²(l) transmitted from antenna1632 b. STTD decoding may then be performed on ŝ¹(l) and ŝ²(l) to obtainsymbol estimates ŝ(l) , which are estimates of data symbols s(l) forwireless device 120.

In another embodiment, x¹(n) is recovered by treating x²(n) as noise,and x²(n) is recovered by treating x¹(n) as noise. For this embodiment,the equalization to recover x^(b)(n), for bε{1, 2}, may be performedusing any of the equalization schemes described above.

For clarity, the equalization techniques have been specificallydescribed for an LMMSE filter and with the equalizer coefficientsderived in the frequency domain. These techniques may also be used forother types of filters. In general, the equalizer coefficients may bederived in the time domain or frequency domain. Furthermore, theequalizer coefficients may be derived using various techniques such asLMMSE, least mean square (LMS), recursive least square (RLS), directmatrix inversion (DMI), zero-forcing, and other techniques. LMS, RLS,and DMI are described by Simon Haykin in a book entitled “AdaptiveFilter Theory”, 3rd edition, Prentice Hall, 1996.

The equalization techniques described herein may be implemented byvarious means. For example, these techniques may be implemented inhardware, firmware, software, or a combination thereof. For a hardwareimplementation, the processing units used to perform equalization may beimplemented within one or more application specific integrated circuits(ASICs), digital signal processors (DSPs), digital signal processingdevices (DSPDs), programmable logic devices (PLDs), field programmablegate arrays (FPGAs), processors, controllers, micro-controllers,microprocessors, electronic devices, other electronic units designed toperform the functions described herein, or a combination thereof.

For a firmware and/or software implementation, the equalizationtechniques may be implemented with modules (e.g., procedures, functions,and so on) that perform the functions described herein. The firmwareand/or software codes may be stored in a memory (e.g., memory 292 inFIG. 2) and executed by a processor (e.g., processor 290). The memorymay be implemented within the processor or external to the processor.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. An apparatus comprising: at least one processor configured to selecta sampling time instant from among multiple sampling time instants of aninput signal, to derive equalizer coefficients for the selected samplingtime instant in accordance with subsampled impulse response channelestimates of the input signal and covariance values of subsampled inputsignal samples of input signal for the selected sampling time instant,and to filter input samples for the selected sampling time instant withthe equalizer coefficients; and a memory coupled to the at least oneprocessor.
 2. The apparatus of claim 1, wherein the at least oneprocessor is configured to determine energies of multiple channelimpulse response estimates for the multiple sampling time instants, andto select the sampling time instant with a largest energy among themultiple sampling time instants.
 3. The apparatus of claim 1, whereinthe at least one processor is configured to derive a channel impulseresponse estimate for the selected sampling time instant, and to derivethe equalizer coefficients based on the channel impulse responseestimate.
 4. The apparatus of claim 1, wherein the at least oneprocessor is configured to derive a channel impulse response estimatefor the selected sampling time instant, to determine covariance valuesfor the input samples for the selected sampling time instant, and toderive the equalizer coefficients based on the channel impulse responseestimate and the covariance values.
 5. The apparatus of claim 1, whereinthe at least one processor is configured to derive a channel impulseresponse estimate for the selected sampling time instant, to derive achannel frequency response estimate based on the channel impulseresponse estimate, to determine time-domain covariance values for theinput samples for the selected sampling time instant, to determinefrequency-domain covariance values based on the time-domain covariancevalues, to derive frequency-domain equalizer coefficients based on thechannel frequency response estimate and the frequency-domain covariancevalues, and to derive time-domain equalizer coefficients based on thefrequency-domain equalizer coefficients.
 6. The apparatus of claim 1,wherein the at least one processor is configured to derive an effectivechannel impulse response estimate between multiple transmit antennas andat least one receive antenna for the selected sampling time instant, andto derive the equalizer coefficients based on the effective channelimpulse response estimate.
 7. The apparatus of claim 1, wherein the atleast one processor is configured to derive the equalizer coefficientsbased on a linear minimum mean square error (LMMSE) technique.
 8. Theapparatus of claim 1, wherein the at least one processor is configuredto receive input samples at multiple times chip rate, to demultiplex theinput samples into multiple sequences for the multiple sampling timeinstants, one sequence for each sampling time instant, and to filter thesequence of input samples for the selected sampling time instant withthe equalizer coefficients.
 9. The apparatus of claim 1, wherein themultiple sampling time instants comprise first and second sampling timeinstants, and wherein the at least one processor is configured toreceive input samples at twice chip rate, to demultiplex the inputsamples into on-time samples tor the first sampling time instant andlate samples for the second sampling time instant, to select either thefirst or second sampling time instant, to filter the on-time sampleswith the equalizer coefficients if the first sampling time instant isselected, and to filter the late samples with the equalizer coefficientsif the second sampling time instant is selected.
 10. The apparatus ofclaim 1, wherein the at least one processor is further configured tofilter input samples for the selected sampling time instant with theequalizer coefficients and with the subsampled input signal samples. 11.A method comprising: selecting a sampling time instant from amongmultiple sampling time instants of an input signal; deriving equalizercoefficients for the selected sampling time instant in accordance withsubsampled impulse response channel estimates of the input signal andcovariance values of subsampled input signal samples of the input signalfor the selected sampling time instant; and filtering input samples forthe selected sampling time instant with the equalizer coefficients. 12.The method of claim 11, wherein the selecting the sampling time instantcomprises determining energies of multiple channel impulse responseestimates for the multiple sampling time instants, and selecting thesampling time instant with a largest energy among the multiple samplingtime instants.
 13. The method of claim 11, wherein the filtering theinput samples comprises receiving input samples at multiple times chiprate, demultiplexing the input samples into multiple sequences for themultiple sampling time instants, one sequence for each sampling timeinstant, and filtering the sequence of input samples for the selectedsampling time instant with the equalizer coefficients.
 14. The method ofclaim 11, wherein filtering input samples comprises filtering inputsamples for the selected sampling time instant with the equalizercoefficients and with the subsampled input signal samples.
 15. Anapparatus comprising: means for selecting a sampling time instant fromamong multiple sampling time instants of an input signal; means forderiving equalizer coefficients for the selected sampling time instantin accordance with subsampled impulse response channel estimates of theinput signal and covariance values of subsampled input signal samples ofthe input signal for the selected sampling time instant; and means forfiltering input samples for the selected sampling time instant with theequalizer coefficients.
 16. The apparatus of claim 15, wherein the meansfor selecting the sampling time instant comprises means for determiningenergies of multiple channel impulse response estimates for the multiplesampling time instants, and means for selecting the sampling timeinstant with a largest energy among the multiple sampling time instants.17. The apparatus of claim 15, wherein the means for filtering the inputsamples comprises means for receiving input samples at multiple timeschip rate, means for demultiplexing the input samples into multiplesequences for the multiple sampling time instants, one sequence for eachsampling time instant, and means for filtering the sequence of inputsamples for the selected sampling time instant with the equalizercoefficients.
 18. The apparatus of claim 15, wherein the means forfiltering comprises means for filtering input samples for the selectedsampling time instant with the equalizer coefficients and with thesubsampled input signal samples.
 19. A computer program product residingon a non-transitory processor-readable medium of a wirelesscommunication device and comprising instructions configured to cause aprocessor to: select a sampling time instant from among multiplesampling time instants of an input signal to the device; deriveequalizer coefficients for the selected sampling time instant inaccordance with subsampled impulse response channel estimates of theinput signal and covariance values of subsampled input signal samples ofthe input signal for the selected sampling time instant; and filterinput samples for the selected sampling time instant with the equalizercoefficients.
 20. The computer program product of claim 19, wherein theinstructions configured to cause the processor to select the samplingtime instant are configured to cause the processor to: determineenergies of multiple channel impulse response estimates for the multiplesampling time instants, and select the sampling time instant with alargest energy among the multiple sampling time instants.
 21. Thecomputer program product of claim 19, wherein the instructionsconfigured to cause the processor to filter the input samples areconfigured to cause the processor to: receive input samples at multipletimes chip rate, demultiplex the input samples into multiple sequencesfor the multiple sampling time instants, one sequence for each samplingtime instant, and filter the sequence of input samples for the selectedsampling time instant with the equalizer coefficients.
 22. The computerprogram product of claim 18, wherein the instructions configured tocause the processor to filter the input samples are further configuredto cause the processor to filter input samples for the selected samplingtime instant with the equalizer coefficients and with the subsampledinput signal samples.